An MGF-Based Performance Analysis of Opportunistic Relay Selection with Outdated CSI

Up to now, a closed-form expression of the ergodic capacity for amplify-and-forward opportunistic relaying in the presence of outdated channel state information(CSI) is still not available in the literature. That is mainly due to the mathematical intractability in the conventional performance analysis through manipulations of probability density function (PDF). In this paper, therefore, we take advantage of a novel mathematical approach based on moment generating function (MGF) to evaluate the performance. MGF of the end-to-end signal-to-noise ratio for opportunistic relaying over independent and identically distributed Rayleigh channels with outdated CSI is given. Then, the closed-form expressions of ergodic capacity and outage probability are derived directly from MGF without any involvement of PDF. Finally, Monte-Carlo simulations are set up to corroborate the validity of the theoretical analysis.